Section 2.4 Linear Inequalities and Applications 87 The following table shows some inequalities and their equivalent interval and set-builder notations for real numbers a and b. Inequality Graph Interval Notation Set-Builder Notation x > a a (a, ∞) 5xux > a6 x ≥ a a a, ∞) 5xux ≥ a6 x < a a (-∞, a) 5xux < a6 x ≤ a a (-∞, a 5xux ≤ a6 a < x < b a b (a, b) 5xua < x < b6 a ≤ x ≤ b a b a, b 5xua ≤ x ≤ b6 a < x ≤ b a b (a, b 5xua < x ≤ b6 a ≤ x < b a b a, b) 5xua ≤ x < b6 Procedure: Graphing the Solution Set of an Inequality Step 1: Shade the portion of the number line that contains numbers that satisfy the inequality. Step 2: Determine the appropriate symbol on the endpoint of the solution set. a. If the endpoint of the solution set is a solution of the inequality, place a bracket on this number (a closed-circle can also be used to represent this). b. If the endpoint of the solution set is not a solution of the inequality, place a parenthesis on this number (an open-circle can also be used to represent this). Procedure: Writing the Solution Set of an Inequality in Interval Notation or Set-Builder Notation Interval Notation Step 1: Begin the interval with the smallest endpoint in the set. Use a parenthesis if this endpoint is not included or a bracket if it is included. Step 2: End the interval with the largest endpoint in the set. Use a parenthesis if this endpoint is not included or a bracket if it is included. Set-Builder Notation Write the set as 5xuput the inequality here6.
hendricks_intermediate_algebra_1e_ch1_3
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